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This notion of dependency seems too binary to me. Concretely, let’s modify your example from the beginning so that \(P_3\) must grant an extra \(10^{-10}\) utility to either \(P_1\) or \(P_2\), and gets to decide which. Now, everyone’s utility depends on everyone’s actions, and the game is still zero-sum, so again, so any strategy profile with \(p=q\) will be a stratified Pareto optimum. But it seems like \(P_1\) and \(P_2\) should ignore still ignore \(P_3\).

by Scott Garrabrant 358 days ago | link

I agree with this. I think that the most interesting direction of future work is to figure out how to have better notions of dependency. I plan on writing some on this in the future, but basically we have not successfully figured out how to deal with this.






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